Vector Algebra And Calculus Cheat Sheet Page 9
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28Vector Quadruple Product (a × b) × (c × d)
2.8
• We have just learned that
[p × (q × r)] = (p · r)q
(p · q)r
⇒ (a × b) × (c × d) = ??
• Regarding a × b as a single vector
⇒ vqp must be a linear combination of c and d
• Regarding c × d as a single vector
⇒ vqp must be a linear combination of a and b.
• Substituting in carefully (you check ...)
(a × b) × (c × d) = [(a × b) · d]c
[(a × b) · c]d
= [(c × d) · a]b
[(c × d) · b]a
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